Optical modulator

ABSTRACT

A single drive type optical modulator has good high-frequency characteristics and reduced wavelength chirp of the modulated light. An optical modulator is provided with a Mach-Zehnder optical waveguide including first and second optical waveguides, a buffer layer covering the first and second optical waveguides, and an electrode layer including first and second ground electrodes and a signal electrode positioned between the first and second ground electrodes in a plan view. The signal electrode has a first lower surface covering the first optical waveguide through the buffer layer, the first ground electrode has a first lower surface covering the second optical waveguide through the buffer layer and a second lower surface positioned above the first lower surface, and a gap between the signal electrode and the second ground electrode that is larger than a gap between the signal electrode and the first ground electrode.

TECHNICAL FIELD

The present invention relates to an optical modulator used in the fieldsof optical communication and optical instrumentation and, moreparticularly, to an electrode structure of a Mach-Zehnder opticalmodulator.

BACKGROUND ART

As the use of the Internet spreads, the amount of data communicated israpidly increasing, making the optical fiber communication veryimportant. In the optical fiber communication, electric signals areconverted into optical signals, and the optical signals are transmittedthrough optical fibers. The optical fiber communication is characterizedin that the signals are transmitted in the broad band, with a smallloss, and are not affected by noise.

Known as systems for converting electric signals into optical signalsare the direct modulation system using a semiconductor laser and theexternal modulation system using optical modulators. The directmodulation system need not use the optical modulators and its runningcost is low, but cannot achieve high-speed modulation. This is why theexternal modulation system is used in high-speed and long-distance datacommunication.

As the optical modulator, a Mach-Zehnder optical modulator in which anoptical waveguide is formed by Ti (titanium) diffusion in the vicinityof the surface of a single-crystal lithium niobate substrate has beenpractically used (see, e.g., Patent Document 1). Although high-speedoptical modulators having a modulation speed of 40 Gb/s or more arecommercially available, they have a major drawback that the entirelength thereof is as long as about 10 cm. The Mach-Zehnder opticalmodulator is an optical modulator that uses an optical waveguide(Mach-Zehnder optical waveguide) having a Mach-Zehnder interferometerstructure. The Mach-Zehnder interferometer is a device that separateslight emitted from one light source into two beams, makes the two beamspass through different paths, and then recombines the two beams to causeinterference, and the Mach-Zehnder optical modulator applying theMach-Zehnder interferometer is used for generating various modulatedlights.

On the other hand, Patent Documents 2 to 4 disclose a Mach-Zehnderoptical modulator using a c-axis oriented lithium niobate film. Theoptical modulator using the lithium niobate film achieves significantreduction in size and driving voltage as compared with the opticalmodulator using the lithium niobate single-crystal substrate.

As described in Patent Document 1, conventional Mach-Zehnder opticalmodulators have a problem of deterioration in signal waveform due to achange in wavelength of a modulated light called wavelength chirp.Electric fields to be applied to respective parallel waveguides differfrom each other in strength due to a difference in arrangement of asignal electrode relative to the parallel waveguides, with the resultthat a variation amount (Δn_(s)) of the refractive index of onewaveguide that is close to the signal electrode becomes larger than avariation amount (Δn_(G)) of the refractive index of the other waveguidethat is far from the signal electrode. This makes the phase changes oflights propagating in the respective parallel waveguides differ inabsolute value, so that the wavelength chirp occurs to degrade a signalwaveform after transmission when a signal is changed from “0” to “1” orfrom “1” to “0”.

The cross-sectional structure of a conventional optical modulator 600described in Patent Document 2 is illustrated in FIG. 9A. A pair ofoptical waveguides 22 a and 22 b of a lithium niobate film are formed ona sapphire substrate 21, and a signal electrode 24 a and a groundelectrode 24 b are disposed above the optical waveguides 22 a and 22 b,respectively, through a buffer layer 23. The optical modulator 600 is ofa so-called single drive type having one signal electrode 24 a, and thesignal electrode 24 a and ground electrode 24 b have a symmetricalstructure, so that electric fields to be applied to the opticalwaveguides 22 a and 22 b are the same in magnitude and opposite inpolarity, preventing the wavelength chirp of a modulated light fromoccurring. However, it does not operate at high frequencies because thearea of the ground electrode 24 b is small.

The cross-sectional structure of a conventional optical modulator 700described in Patent Document 3 is illustrated in FIG. 9B. Two signalelectrodes 24 a 1 and 24 a 2 are disposed above a pair of opticalwaveguides 22 a and 22 b of a lithium niobate film, respectively,through a buffer layer 23, and three ground electrodes 24 c 24 d, and 24e are disposed so as to be separated from the signal electrodes 24 a 1and 24 a 2. When voltages same in magnitude and opposite in polarity areapplied to the two signal electrodes 24 a 1 and 24 a 2, respectively,electric fields to be applied to the optical waveguides 22 a and 22 bbecome the same in magnitude and opposite in polarity, preventing thewavelength chirp of a modulated light from occurring. Further, theamount of the chirp can be adjusted by adjusting voltage to be appliedto the pair of optical waveguides 22 a and 22 b. Furthermore, since theareas of the left and right ground electrodes 24 c and 24 d aresufficiently ensured, it has a structure operable at high frequencies.However, the optical modulator 700 is of a dual drive type having twosignal electrodes 24 a and 24 b, which complicates an electrodestructure. Further, it is necessary to provide two input connectors forhigh-frequency electric signals and to apply voltages to both the signalelectrodes while controlling the phase of the electric signal in whichdata has been inversed, and this complicates the circuit configurationof a drive system.

CITATION LIST Patent Document

[Patent Document 1] Japanese Patent No. 4,485,218

[Patent Document 2] Japanese Patent Application Laid-Open No.2006-195383

[Patent Document 3] Japanese Patent Application Laid-Open No.2014-006348

[Patent Document 4] Japanese Patent Application Laid-Open No.2015-118371

SUMMARY OF INVENTION Problem to be Solved by Invention

The cross-sectional structure of an optical modulator 800 of 2 a singledrive type capable of operating at high frequencies is illustrated inFIG. 9C. In the optical modulator 800, first and second groundelectrodes 24 b and 24 c are provided to the left and right of a singlesignal electrode 24 a, and each area of the ground electrodes issufficiently ensured, it has a structure operable at high frequencies.However, the planar size of the ground electrode 24 b is large, makingit difficult for an electric field to concentrate on an opticalwaveguide 22 b, with the result that an electric field to be applied tothe optical waveguide 22 a is larger in magnitude than an electric fieldto be applied to the optical waveguide 22 b, so that the wavelengthchirp of a modulated light becomes recognized as a problem.

It is therefore an object of the present invention to provide a singledrive type optical modulator having good high-frequency characteristicsand reduced wavelength chirp of the modulated light.

Means for Solving Problem

To solve the above problems, an optical modulator according to thepresent invention includes a Mach-Zehnder optical waveguide includingfirst and second optical waveguides, a buffer layer covering the firstand second optical waveguides, and an electrode layer including firstand second ground electrodes and a signal electrode positioned betweenthe first and second ground electrodes in a plan view. The signalelectrode has a first lower surface covering the first optical waveguide through the buffer layer. The first ground electrode has a firstlower surface covering the second optical waveguide through the bufferlayer and a second lower surface positioned above the first lowersurface thereof. A gap between the signal electrode and the secondground electrode is larger than a gap between the signal electrode andthe first ground electrode.

According to the present invention, a difference between the magnitudesof electric fields to be applied respectively to the pair of opticalwaveguides caused due to a difference in size between the signalelectrode and the first ground electrode is minimized, whereby thewavelength chirp of the modulated light can be reduced. Further,existence of the second ground electrode allows a reduction in radiationloss to thereby obtain good high-frequency characteristics. Further,making the gap between the signal electrode and the second groundelectrode larger than the gap between the signal electrode and the firstground electrode allows a reduction in the difference between themagnitudes of electric fields to be applied respectively to the pair ofoptical waveguides caused due to influence of the second groundelectrode to thereby reduce the wavelength chirp of the modulated light.

In the present invention, a width of the first lower surface of thesignal electrode is preferably larger than a width of the first lowersurface of the first ground electrode. This allows a further reductionin the difference between the magnitudes of electric fields to beapplied respectively to the pair of optical waveguides caused due toinfluence of the second ground electrode to thereby reduce thewavelength chirp of the modulated light.

In the present invention, the signal electrode preferably further has asecond lower surface positioned above the first lower surface thereof.This allows an electric field to be concentrated on the first opticalwaveguide and allows achievement of balance between the electric fieldsto be applied respectively to the first and second optical waveguides.

In the present invention, the width of the first lower surface of thesignal electrode and the width of the first lower surface of the firstground electrode are preferably larger than the widths of the first andsecond optical waveguides. This allows the signal electrode and thefirst ground electrode to reliably face the first and second opticalwaveguides, respectively, while enhancing concentration of an electricfield on the pair of optical waveguides.

It is preferable that the optical modulator according to the presentinvention further includes an insulating layer provided between thebuffer layer and the electrode layer, the insulating layer has first andsecond openings positioned above the first and second opticalwaveguides, respectively, the signal electrode includes an upper partformed in the electrode layer and a lower part embedded in the firstopening, the first ground electrode includes an upper part formed in theelectrode layer and a lower part embedded in the second opening, and thewidth of the upper part of the first ground electrode is larger than thewidth of the lower part of the first ground electrode. This allows anelectrode structure having first and second lower surfaces different inheight to be easily achieved.

In the present invention, the width of the upper part of the signalelectrode is preferably larger than the width of the lower part of thesignal electrode and is also preferably equal thereto. In either case,it is possible to provide a single drive type optical modulator havinggood high-frequency characteristics and reduced wavelength chirp of themodulated light.

In the present invention, at least a part of the insulating layerexisting at the lower portion of an electrode isolation region betweenthe lower part of the signal electrode and the lower part of the firstground electrode may be removed. Further, a part of the buffer layerexisting below the electrode isolation region may be removed togetherwith the part of the insulating layer. Further, the optical modulatoraccording to the present invention may further include a waveguide layerhaving ridges constituting the first and second optical waveguides,respectively, and a protective layer covering the upper surface of thewaveguide layer excluding portions where the ridges are formed. Thebuffer layer may cover the upper surfaces of the respective ridges andthe upper surface of the protective layer. A part of the protectivelayer existing below the electrode isolation region may be removedtogether with the part of the insulating layer and part of the bufferlayer. With the above configuration, it is possible to match theeffective refractive index of a traveling-wave electrode and theeffective refractive index of light to achieve good speed matching,whereby an optical modulator having good high-frequency characteristicscan be achieved.

In the present invention, it is preferable that the Mach-Zehnder opticalwaveguide has at least one linear section and at least one curvedsection, the first lower surface of the signal electrode covers thefirst optical waveguide at the linear section through the buffer layer,and the first lower surface of the first ground electrode covers thesecond optical waveguide at the linear section through the buffer layer.In this case, it is preferable that the linear sections includes firstto third linear sections arranged in parallel to one another, the curvedsections includes a first curved section connecting the first and secondlinear sections and a second curved section connecting the second andthird linear sections, the first lower surface of the signal electrodecovers the first optical waveguide at least one of the first to thirdlinear sections through the buffer layer, and the first lower surface ofthe first ground electrode covers the second optical waveguide at leastone of the first to third linear sections through the buffer layer. Withthe above configuration, the optical waveguide can have a foldingstructure to reduce an element length. Particularly, an opticalwaveguide formed of the lithium niobate film has small loss even whenthe curvature radius thereof is reduced up to about 50 μm, so thateffects of the present invention are remarkable.

In the present invention, it is preferable that the Mach-Zehnder opticalwaveguide is formed of a lithium niobate film formed on a substrate, andthe c-axis of the lithium niobate film is oriented in a directionperpendicular to a main surface of the substrate. When the Mach-Zehnderoptical waveguide is formed using the lithium niobate film, the opticalwaveguide can be made very thin and narrow in line width, whereby asmall-sized and high-quality optical modulator can be obtained. However,since the optical waveguide is thin and narrow in line width, a problemof the electric field concentration is conspicuous. However, accordingto the present invention, such a problem can be solved, and a singledrive type optical modulator having good high-frequency characteristicsand reduced wavelength chirp of the modulated light can be achieved.

Advantageous Effects of Invention

According to the present invention, there can be provided a single drivetype optical modulator having good high-frequency characteristics andreduced wavelength chirp of the modulated light.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1A and 1B are plan views of an optical modulator 100 according toa first embodiment of the present invention, wherein FIG. 1A illustratesonly optical waveguides, and FIG. 1B illustrates the entire of theoptical modulator 100 including a traveling-wave electrode.

FIG. 2 is a schematic cross-sectional view of the optical modulator 100taken along line A-A′ of FIGS. 1A and 1B.

FIG. 3 is a schematic cross-sectional view illustrating theconfiguration of an optical modulator 200 according to a secondembodiment of the present invention.

FIG. 4A is a schematic cross-sectional view illustrating theconfiguration of an optical modulator 300 according to a thirdembodiment of the present invention, and FIG. 4B is a schematiccross-sectional view illustrating the configuration of an opticalmodulator 400 according to a fourth embodiment of the present invention.

FIGS. 5A and 5B are plan views of an optical modulator 500 according toa fifth embodiment of the present invention. FIG. 5A illustrates onlythe optical waveguide, and FIG. 5B illustrates the entire configurationof the optical modulator 500 including the traveling-wave electrode.

FIGS. 6A and 6B each illustrate an equipotential surface which is anexample of a result obtained by the simulations, wherein FIG. 6Aillustrates a result when T is set to 0 μm, and FIG. 6B illustrates aresult when T is set to 6 μm.

FIG. 7 is a graph illustrating a calculation result of the wavelengthchirp α.

FIG. 8 is a graph illustrating a calculation result of the wavelengthchirp α.

FIGS. 9A to 9C are schematic cross-sectional views illustrating thestructure of conventional optical modulators.

MODE FOR CARRYING OUT THE INVENTION

Preferred embodiment of the present invention will be described indetail below with reference to the accompanying drawings.

FIGS. 1A and 1B are plan views of an optical modulator 100 according toa first embodiment of the present invention. FIG. 1A illustrates onlyoptical waveguides, and FIG. 1B illustrates the entire of the opticalmodulator 100 including a traveling-wave electrode.

As illustrated in FIGS. 1A and 1B, the optical modulator 100 includes aMach-Zehnder optical waveguide 10 formed on a substrate 1 and havingfirst and second optical waveguides 10 a and 10 b provided in parallelto each other, a signal electrode 7 provided along the first opticalwaveguide 10 a, a first ground electrode 8 provided along the secondoptical waveguide 10 b, and a second ground electrode 9 provided on theside opposite to the first ground electrode 8 as viewed from the signalelectrode 7.

The Mach-Zehnder optical waveguide 10 is an optical waveguide having aMach-Zehnder interferometer structure. The Mach-Zehnder opticalwaveguide 10 has the first and second optical waveguides 10 a and 10 bwhich are branched from a single input optical waveguide 10 i at abranch section 10 c, and the first and second optical waveguides 10 aand 10 b are combined into a single output optical waveguide 10 o at amultiplexing section 10 d. An input light Si is branched at the branchsection 10 c. The branched lights travel through the first and secondoptical waveguides 10 a and 10 b and then multiplexed at themultiplexing section 10 d. The multiplexed light is output from theoutput optical waveguide 10 o as a modulated light So.

The signal electrode 7 is positioned between the first and second groundelectrodes 8 and 9 in a plan view. One end 7 e of the signal electrode 7serves as a signal input end, and the other end 7 g thereof is connectedto the first and second ground electrodes 8 and 9 through terminalresistors 12. As a result, the signal electrode 7 and first and secondground electrodes 8 and 9 function as a coplanar traveling-waveelectrode. Although details will be described later, the signalelectrodes 7 and the first ground electrode 8 each have a two-layerstructure. A lower part 7 b of the signal electrode 7 denoted by thedashed line overlaps the first optical waveguide 10 a in a plan view,and a lower part 8 b of the first ground electrode 8 denoted by thedashed line overlaps the second optical waveguide 10 b in a plan view.

An electric signal (modulated signal) is input to the one end 7 e of thesignal electrode 7. The first and second optical waveguides 10 a and 10b are made of a material, such as lithium niobate having electroopticeffect, so that the refractive indices of the first and second opticalwaveguides 10 a and 10 b are changed with +Δn and −Δn by an electricfield applied to the first and second optical waveguides 10 a and 10 b,with the result that a phase difference between the pair of opticalwaveguides changes. A signal light modulated by the change in the phasedifference is output from the output optical waveguide 10 o.

As described above, the optical modulator 100 according to the presentembodiment is of a single drive type having one signal electrode 7, sothat a sufficient area for the first ground electrode 8 can be ensured,allowing operation at high frequencies. Further, by disposing the secondground electrode 9 on the side opposite to the first ground electrode 8across the signal electrode 7, radiation loss can be reduced, wherebybetter high-frequency characteristics can be obtained.

FIG. 2 is a schematic cross-sectional view of the optical modulator 100taken along line A-A′ of FIGS. 1A and 1B.

As illustrated in FIG. 2, the optical modulator 100 according to thepresent embodiment has a multilayer structure including a substrate 1, awaveguide layer 2, a protective layer 3, a buffer layer 4, an insulatinglayer 5, and an electrode layer 6 which are laminated in this order. Thesubstrate 1 is, e.g., a sapphire substrate, and the waveguide layer 2made of a lithium niobate film is formed on the surface of the substrate1. The waveguide layer 2 has the first and second optical waveguides 10a and 10 b each formed by a ridge 2 r. A width W₀ of each of the firstand second optical waveguides 10 a and 10 b can be set to, e.g., 1 μm.

The protective layer 3 is formed in an area not overlapped with thefirst and second optical waveguides 10 a and 10 b in a plan view. Theprotective layer 3 covers the entire area of the upper surface of thewaveguide layer 2 excluding areas where the ridges 2 r are formed, andthe side surfaces of the ridges 2 r are also covered with the protectivelayer 3, so that scattering loss due to the roughness of the sidesurfaces of the ridges 2 r can be prevented. The thickness of theprotective layer 3 is substantially equal to the height of the ridge 2 rof the waveguide layer 2. The material of the protective layer 3 is notparticularly limited, but silicon oxide (SiO₂), for example, can beused.

The buffer layer 4 is formed on the upper surfaces of the ridges 2 r ofthe waveguide layer 2 so as to prevent light propagating through thefirst and second optical waveguides 10 a and 10 b from being absorbed bythe signal electrode 7 or first ground electrode 8. As the buffer layer4, a material, such as silicon oxide (SiO₂) or aluminum oxide (Al₂O₃),having a lower refractive index than the waveguide layer 2 may be used,and the thickness thereof may be about 0.2 μm to 1 μm. In the presentembodiment, although the buffer layer 4 covers not only the uppersurfaces of the respective first and second optical waveguides 10 a and10 b, but also the entire underlying surface including the upper surfaceof the protective layer 3, it may be patterned so as to selectivelycover only the vicinity of the upper surfaces of the first and secondoptical waveguides 10 a and 10 b.

The insulating layer 5 is provided to form a level difference on thelower surface of the traveling-wave electrode. Openings (slits) areformed in respective areas of the insulating layer 5 overlapping therespective first and second optical waveguides 10 a and 10 b to exposethe upper surface of the buffer layer 4 therethrough. A part of theelectrode layer 6 is embedded in the openings, with the result that thelevel differences are formed on the lower surfaces of the signalelectrode 7 and the first ground electrode 8, respectively. A thicknessT of the insulating layer 5 is preferably equal to or larger than 1 μm.When the thickness of the insulating layer 5 is equal to or larger than1 μm, an effect of the formation of the level difference on the lowersurfaces of the respective signal electrode 7 and first ground electrode8 can be obtained.

The electrode layer 6 is provided with the signal electrode 7, firstground electrode 8, and second ground electrode 9. The signal electrode7 is provided overlapping the ridge 2 r corresponding to the firstoptical waveguide 10 a so as to modulate light traveling inside thefirst optical waveguide 10 a and opposed to the first optical waveguide10 a through the buffer layer 4. The first ground electrode 8 isprovided overlapping the ridge 2 r corresponding to the second opticalwaveguide 10 b so as to modulate light traveling inside the secondoptical waveguide 10 b and opposed to the second optical waveguide 10 bthrough the buffer layer 4. The second ground electrode 9 is provided onthe side opposite to the first ground electrode 8 across the signalelectrode 7.

Although the waveguide layer 2 is not particularly limited as long as itis an electrooptic material, it is preferably made of lithium niobate(LiNbO₃). This is because lithium niobate has a large electroopticconstant and is thus suitable as the constituent material of an opticaldevice such as an optical modulator. Hereinafter, the configuration ofthe present invention when the waveguide layer 2 is made of lithiumniobate will be described in detail.

Although the substrate 1 is not particularly limited in material as longas it has a lower refractive index than the lithium niobate film, thesubstrate 1 is preferably a substrate on which the lithium niobate filmcan be formed as an epitaxial film. Specifically, the substrate 1 ispreferably a sapphire single-crystal substrate or a siliconsingle-crystal substrate. The crystal orientation of the single-crystalsubstrate is not particularly limited. The lithium niobate film can beeasily formed as a c-axis oriented epitaxial film on single-crystalsubstrates of various crystal orientations. Since the c-axis orientedlithium niobate film has three-fold symmetry, the underlyingsingle-crystal substrate preferably has the same symmetry. Thus, it ispreferable that the substrate has c-plane if it is a sapphiresingle-crystal substrate, or (111) plane if it is a siliconsingle-crystal substrate.

The term “epitaxial film”, as used herein, refers to a film having thecrystal orientation of the underlying substrate or film. The crystal ofan epitaxial film is uniformly oriented along the X-axis and Y-axis onthe film surface and along the Z-axis in the thickness direction. Forexample, the existence of an epitaxial film can be confirmed by firstmeasuring the peak intensity at the orientation position by 2θ-θ X-raydiffraction and secondly observing poles.

Specifically, first, in the 2θ-θ X-ray diffraction measurement, all thepeak intensities except for the target plane must be 10% or less,preferably 5% or less, of the maximum peak intensity on the targetplane. For example, in a c-axis oriented epitaxial lithium niobate film,the peak intensities except for a (00L) plane are 10% or less,preferably 5% or less, of the maximum peak intensity on the (00L) plane.(00L) is a general term for (001), (002), and other equivalent planes.

Secondly, poles must be observed in the measurement. Under the conditionwhere the peak intensities are measured at the first orientationposition, only the orientation in a single direction is proved. Even ifthe first condition is satisfied, in the case of nonuniformity in thein-plane crystalline orientation, the X-ray intensity is not increasedat a particular angle, and poles cannot be observed. Since LiNbO₃ has atrigonal crystal system, single-crystal LiNbO₃ (014) has 3 poles. Forthe lithium niobate film, it is known that crystals rotated by 180°about the c-axis are epitaxially grown in a symmetrically-coupled twincrystal state. In this case, three poles are symmetrically-coupled toform six poles. When the lithium niobate film is formed on asingle-crystal silicon substrate having a (100) plane, the substrate hasfour-fold symmetry, and 4×3=12 poles are observed. In the presentinvention, the lithium niobate film epitaxially grown in the twincrystal state is also considered to be an epitaxial film.

The lithium niobate film has a composition of LixNbAyOz. A denotes anelement other than Li, Nb, and O. The number x ranges from 0.5 to 1.2,preferably 0.9 to 1.05. The number y ranges from 0 to 0.5. The number zranges from 1.5 to 4, preferably 2.5 to 3.5. Examples of the element Ainclude K, Na, Rb, Cs, Be, Mg, Ca, Sr, Ba, Ti, Zr, Hf, V, Cr, Mo, W, Fe,Co, Ni, Zn, Sc, and Ce, alone or in combination.

The lithium niobate film preferably has a thickness of equal to orsmaller than 2 μm. This is because a high-quality lithium niobate filmhaving a thickness larger than 2 μm is difficult to form. The lithiumniobate film having an excessively small thickness cannot completelyconfine light, allowing light to leak to the substrate or the bufferlayer and thus to be guided therethrough. Application of an electricfield to the lithium niobate film may therefore cause a small change inthe effective refractive index of the optical waveguides (1 a and 1 b).Thus, the lithium niobate film preferably has a thickness that is atleast approximately one-tenth of the wavelength of light to be used.

It is desirable to form the lithium niobate film by a film formingmethod such as sputtering, CVD, or sol-gel process. If the c-axis of thelithium niobate film is oriented perpendicular to the main surface ofthe single-crystal substrate, an electric field is applied parallel tothe c-axis, thereby changing the optical refractive index in proportionto the intensity of the electric field. If the single-crystal substrateis sapphire, the lithium niobate film is formed by epitaxial growthdirectly on the sapphire single-crystal substrate. If the single-crystalsubstrate is silicon, the lithium niobate film is formed by epitaxialgrowth on a cladding layer (not shown) formed on the substrate. Thecladding layer (not shown) is made of material which has a lowerrefractive index than the lithium niobate film and should be suitablefor epitaxial growth. For example, if the cladding layer (not shown) ismade of Y₂O₃, a lithium niobate film of high quality can be formed.

As a formation method for the lithium niobate film, there is known amethod of thinly polishing or slicing the lithium niobate single crystalsubstrate. This method is advantageous in that the same characteristicsas the single crystal can be obtained and can be applied to the presentinvention.

The signal electrode 7 has a two-layer structure and has an upper part 7a formed in the electrode layer 6 and a lower part 7 b embedded in anopening (first opening) penetrating the insulating layer 5. The lowerpart 7 b of the signal electrode 7 is positioned at the end portion ofthe upper part 7 a of the signal electrode 7 close to the first groundelectrode 8. Accordingly, a lower surface (first lower surface) S₁₁ ofthe lower part 7 b of the signal electrode 7 is positioned closer to thefirst ground electrode 8 than a lower surface (second lower surface) S₁₂of the upper part 7 a. With this configuration, the first lower surfaceS₁₁ of the signal electrode 7 is in contact with the upper surface ofthe buffer layer 4 above the first optical waveguide 10 a to cover thefirst optical waveguide 10 a through the buffer layer 4. The secondlower surface S₁₂ of the signal electrode 7 is positioned above thefirst lower surface S₁₁ and is not in contact with the buffer layer 4.

A width W₁₁ of the lower part 7 b of the signal electrode 7 in theX-direction (i.e., width of the first lower surface S₁₁) is smaller thana width W₁₀ of the upper part 7 a in the X-direction (i.e., entire widthof the signal electrode 7). The lower part 7 b is formed only near anarea that overlaps the first optical waveguide 10 a in a plan view andis not formed in the other area. Thus, the width W₁₁ of the first lowersurface Sn of the signal electrode 7 is slightly larger than a width W₀of the first optical waveguide 10 a. To concentrate an electric field onthe first optical waveguide 10 a, the width W₁₁ of the first lowersurface S₁₁ of the signal electrode 7 is preferably 1.1 times to 5times, more preferably, 1.5 times to 3 times the width W₀ of the opticalwaveguide 10 a.

The first ground electrode 8 also has a two-layer structure and has anupper part 8 a formed in the electrode layer 6 and a lower part 8 bembedded in an opening (second opening) penetrating the insulating layer5. The lower part 8 b of the first ground electrode 8 is positioned atthe end portion of the upper part 8 a of the first ground electrode 8close to the signal electrode 7. Accordingly, a lower surface (firstlower surface) S₂₁ of the lower part 8 b of the first ground electrode 8is positioned closer to the signal electrode 7 than a lower surface(second lower surface) S₂₂ of the upper part 8 a. With thisconfiguration, the first lower surface S₂₁ of the first ground electrode8 is in contact with the upper surface of the buffer layer 4 above thesecond optical waveguide 10 b to cover the second optical waveguide 10 bthrough the buffer layer 4. The second lower surface S₂₂ of the firstground electrode 8 is positioned above the first lower surface S₂₁ andis not in contact with the buffer layer 4.

A width W₂₁ of the lower part 8 b of the first ground electrode 8 in theX-direction (i.e., width of the first lower surface S₂₁) is smaller thana width W₂₀ of the upper part 8 a in the X-direction (i.e., entire widthof the first ground electrode 8). The lower part 8 b of the first groundelectrode 8 is formed only near an area that overlaps the second opticalwaveguide 10 b in a plan view and is not formed in the other area. Thus,the width W₂₁ of the first lower surface S₂₁ of the first groundelectrode 8 is slightly larger than a width W₀ of the second opticalwaveguide 10 b. Accordingly, the width W₂₁ of the lower part 8 b of thefirst ground electrode 8 in the X-direction is smaller than the widthW₂₂ of the upper part 8 a in the X-direction. To concentrate an electricfield on the second optical waveguide 10 b, the width W₂₁ of the firstlower surface S₂₁ of the first ground electrode 8 is preferably 1.1times to 5 times, more preferably, 1.5 times to 3 times the width W₀ ofthe optical waveguide 10 b.

The second ground electrode 9 is positioned on the side opposite to thefirst ground electrode 8 across the signal electrode 7. The secondground electrode 9 has a single layer structure constituted of only aconductor provided in the electrode layer 6; however, it may have atwo-layer structure like the signal electrode 7 and the first groundelectrode 8.

The width W₂₀ of the upper part 8 a of the first ground electrode 8 islarger than the width W₁₀ of the upper part 7 a of the signal electrode7. Further, a width W₃₀ of the second ground electrode 9 is alsopreferably larger than the width W₁₀ of the upper part 7 a of the signalelectrode 7. By setting each size of the first and second groundelectrodes 8 and 9 larger than the size of the signal electrode 7,radiation loss can be reduced to thereby obtain good high-frequencycharacteristics.

In the cross-sectional structure of FIG. 2 obtained by verticallycutting the first and second optical waveguides 10 a and 10 b, a gap G₃between the signal electrode 7 and the second ground electrode 9 is setlarger than a gap G₂ between the signal electrode 7 and the first groundelectrode 8. The gap between the signal electrode and the groundelectrode refers to the shortest distance therebetween in theX-direction. When the gap G₃ between the signal electrode 7 and thesecond ground electrode 9 is smaller than the gap G₂ between the signalelectrode 7 and the first ground electrode 8, a difference between themagnitudes of electric fields to be applied respectively to the pair ofoptical waveguides becomes large under the influence of the secondground electrode 9, causing the wavelength chirp; however, when the gapG₃ between the signal electrode 7 and the second ground electrode 9 isset larger than the gap G₂ between the signal electrode 7 and the firstground electrode 8, the influence that the second ground electrode 9 hason the electric fields to be applied respectively to the pair of opticalwaveguides can be reduced. This can make the magnitudes of the electricfields to be applied respectively to the pair of optical waveguides asequal as possible to thereby reduce the wavelength chirp.

In the present embodiment, the width W₁₁ of the lower surface S₁₁ of thesignal electrode 7 is preferably larger than the width W₂₁ of the lowersurface S₂₁ of the first ground electrode 8 (W₁₁>W₂₁). When the secondground electrode 9 is disposed adjacent to the signal electrode 7 asdescribed above, radiation loss is reduced to thereby obtain goodhigh-frequency characteristics; however, the electrode structure becomesasymmetric, causing the wavelength chirp. When the second groundelectrode 9 is absent, by making the width W₁₁ of the lower part 7 b ofthe signal electrode 7 and the width W₂₁ of the lower part 8 b of thefirst ground electrode 8 equal to each other (W₁₁=W₁₂), the magnitudesof electric fields to be applied respectively to the pair of opticalwaveguides can be made substantially the equal; however, only by makingW₁₁ and W₂₁ equal to each other when the second ground electrode 9 isdisposed adjacent to the signal electrode 7, the magnitudes of electricfields to be applied respectively to the first and second opticalwaveguides 10 a and 10 b cannot be made substantially equal. However,when W₁₁ is set larger than W₁₂ as described above, the influence of thesecond ground electrode 9 can be reduced to allow the magnitudes ofelectric fields to be applied respectively to the pair of opticalwaveguides to be made substantially equal, whereby the wavelength chirpcan be prevented from occurring.

As described above, in the optical modulator 100 according to thepresent embodiment, the widths W₂₀ and W₃₀ of the respective first andsecond ground electrodes 8 and 9 are larger than the width W₁₀ of thesignal electrode 7, so that radiation loss can be reduced to therebyobtain good high-frequency characteristics. Further, the first groundelectrode 8 is formed into a two-layer structure, and the width W₂₁ ofthe first lower surface S₂₁ of the lower part 8 b is smaller than thewidth W₂₂ of the upper part 8 a, so that an electric field can beconcentrated on the second optical waveguide 10 b, which makes adifference between the magnitudes of electric fields to be appliedrespectively to the pair of optical waveguides small to thereby reducethe wavelength chirp of a modulated light. Furthermore, the width W₁₁ ofthe lower surface S₁₁ of the signal electrode 7 is larger than the widthW₂₁ of the lower part 8 b of the first ground electrode 8, and the gapG₃ between the signal electrode 7 and the second ground electrode 9 islarger than the gap G₂ between the signal electrode 7 and the firstground electrode 8, so that the difference between the magnitudes ofelectric fields to be applied respectively to the pair of opticalwaveguides caused under the influence of the second ground electrode canbe further reduced to thereby further reduce the wavelength chirp of amodulated light.

FIG. 3 is a schematic cross-sectional view illustrating theconfiguration of an optical modulator 200 according to a secondembodiment of the present invention.

As illustrated in FIG. 3, the optical modulator 200 according to thepresent embodiment is featured in that the upper and lower parts 7 a and7 b of the signal electrode 7 have the same width W₁₀ larger than thewidth W₂₁ of the lower part 8 b of the first ground electrode 8(W₁₀>W₂₁). Other configurations of the optical modulator 200 are thesame as those of the optical modulator 100 according to the firstembodiment. Thus, the present embodiment can produce the same effects asin the first embodiment.

In the optical modulator 100 according to the first embodimentillustrated in FIG. 2, the protective layer 3, buffer layer 4, andinsulating layer 5 are each formed on the entire surface excluding theridges 2 r, the lower part 7 b of the signal electrode 7, and the lowerpart 8 b of the first ground electrode 8; however, the parts of theprotective layer 3, buffer layer 4 and insulating layer 5 between thesignal electrode 7 and the first ground electrode 8 may be removed.

FIG. 4A is a schematic cross-sectional view illustrating theconfiguration of an optical modulator 300 according to a thirdembodiment of the present invention, and FIG. 4B is a schematiccross-sectional view illustrating the configuration of an opticalmodulator 400 according to a fourth embodiment of the present invention.

The optical modulator 300 illustrated in FIG. 4A is a first modificationof the optical modulator 100 illustrated in FIG. 2 and is featured inthat a part (part surrounded by the dashed line H₁) of the insulatinglayer 5 existing below an electrode isolation region 6 i between thelower part 7 b of the signal electrode 7 and the lower part 8 b of thefirst ground electrode 8 is removed to expose a part of the uppersurface of the buffer layer 4. The insulating layer 5 may be removedpartially, not completely, from the electrode isolation region 6 i.

The optical modulator 400 illustrated in FIG. 4B is a secondmodification of the optical modulator 100 illustrated in FIG. 2 and isfeatured in that not only a part of the insulating layer 5 existingbelow the electrode isolation region 6 i between the lower part 7 b ofthe signal electrode 7 and the lower part 8 b of the first groundelectrode 8, but also a part (part surrounded by the dashed line H₂) ofa laminated body constituted of the buffer layer 4 and the protectivelayer 3 positioned below the insulating layer 5 is removed to expose apart of the upper surface of the waveguide layer 2. The laminated bodyof the buffer layer 4 and protective layer 3 may be removed partially,not completely, from the electrode isolation region 6 i. Further, boththe buffer layer 4 and protective layer 3 need not be removed, and onlythe buffer layer 4 may be removed together with the insulating layer 5to expose a part of the upper surface of the protective layer 3.

In order for the optical modulator to obtain good high-frequencycharacteristics, the following three factors are important: (1) speedmatching; (2) low electrode loss; and (3) impedance matching. The speedmatching of (1) refers to matching between the speed of light and thespeed of a traveling-wave electrode, and there is a need to match theeffective refractive indices between them. The effective refractiveindex of light is substantially determined by a material used for theoptical waveguide and is not adjustable. On the other hand, theeffective refractive index of the traveling-wave electrode can bereduced by removing the parts of the protective layer 3, buffer layer 4,and insulating layer 5 as illustrated in FIGS. 4A and 4B, that is,adjustable. Further, the effective refractive index can be increased byadding another layer. However, impedance may be changed with a change inthe effective refractive index, so that, actually, it is necessary tooptimize a condition satisfying both the (1) speed matching and (3)impedance matching.

As described above, in the optical modulator 300 according to the thirdembodiment, a part of the insulating layer 5 existing below theelectrode isolation region 6 i between the lower part 7 b of the signalelectrode 7 and the lower part 8 b of the first ground electrode 8 isremoved, so that it is possible to match the effective refractive indexof the traveling-wave electrode and the effective refractive index oflight to achieve good speed matching. Further, in the optical modulator400 according to the fourth embodiment, a part of the insulating layer 5and a part of a laminated body constituted of the buffer layer 4 andprotective layer 3 (or a part of a laminated body constituted of theinsulating layer 5 and buffer layer 4) existing below the electrodeisolation region 6 i between the lower part 7 b of the signal electrode7 and the lower part 8 b of the first ground electrode 8 are removed, sothat it is possible to match the effective refractive index of thetraveling-wave electrode and the effective refractive index of light tothereby achieve good speed matching.

Although the Mach-Zehnder optical waveguide 10 is linearly formed in theoptical modulator 100 according to the first embodiment illustrated inFIG. 1, it may have a curved section.

FIGS. 5A and 5B are plan views of an optical modulator 500 according toa fifth embodiment of the present invention. FIG. 5A illustrates onlythe optical waveguide, and FIG. 5B illustrates the entire configurationof the optical modulator 500 including the traveling-wave electrode.

As illustrated in FIGS. 5A and 5B, the optical modulator 500 accordingto the present embodiment is featured in that the Mach-Zehnder opticalwaveguide 10 is constructed by a combination of linear sections andcurved sections. Specifically, the Mach-Zehnder optical waveguide 10 hasfirst to third linear sections 10 e ₁, 10 e ₂, and 10 e ₃ arrangedparallel to one another, a first curved section 10 f ₁ connecting thefirst and second linear sections 10 e ₁ and 10 e ₂, and a second curvedsection 10 f ₂ connecting the second and third linear sections 10 e ₂and 10 e ₃.

In the optical modulator 500 according to the present embodiment, thecross-sectional structures of the respective linear sections 10 e ₁, 10e ₂, and 10 e ₃ of the Mach-Zehnder optical waveguide 10 taken alongline A-A′ in FIGS. 5A and 5B are each formed into that illustrated inFIG. 2, FIG. 3, FIG. 4A, or FIG. 4B. That is, the first lower surfaceS₁₁ of the signal electrode 7 covers the first optical waveguide 10 a atthe first to third linear sections 10 e ₁, 10 e ₂, and 10 e ₃ throughthe buffer layer 4, and the first lower surface S₂₁ of the first groundelectrode 8 covers the second optical waveguide 10 b at the first tothird linear sections 10 e ₁, 10 e ₂, and 10 e ₃ through the bufferlayer 4. The first lower surface S₁₁ of the signal electrode 7 and thefirst lower surface S₂₁ of the first ground electrode 8 each preferablycover all the first to third linear sections 10 e ₁, 10 e ₂, and 10 e ₃,but may each cover only, e.g., the first linear section 10 e ₁.

In the present embodiment, the input light Si is input to one end of thefirst linear section 10 e ₁, travels from the one end of the firstlinear section 10 e ₁ toward the other end thereof, makes a U-turn atthe first curved section 10 f 1, travels from one end of the secondlinear section 10 e ₂ toward the other end thereof in the directionopposite to that in the first linear section 10 e ₁, makes a U-turn atthe second curved section 10 f ₂, and travels from one end of the thirdlinear section 10 e ₃ toward the other end thereof in the direction sameas that in the first linear section 10 e ₁.

The optical modulator has a problem of a long element length. However,by folding the optical waveguide as illustrated, the element length canbe significantly reduced, obtaining a remarkable effect. Particularly,the optical waveguide formed of the lithium niobate film is featured inthat it has small loss even when the curvature radius thereof is reducedup to about 50 μm and is thus suitable for the present embodiment.

It is apparent that the present invention is not limited to the aboveembodiments, but may be modified and changed without departing from thescope and spirit of the invention.

For example, in the above embodiments, the optical modulator has thepair of optical waveguides 10 a and 10 b each formed of the lithiumniobate film epitaxial grown on the substrate 1; however, the presentinvention is not limited to such a configuration, and the opticalwaveguides may be formed by Ti diffusion in the vicinity of the surfaceof a lithium niobate single-crystal substrate. However, the opticalwaveguide formed of the lithium niobate film can be reduced in width, sothat a problem of the electric field concentration is conspicuous, andthe present invention is more effective. Further, as the waveguide layer2, a semiconductor material, a polymer material, or the like havingelectrooptic effect may be used.

Further, although the lower surfaces of the respective first groundelectrode 8 and signal electrode 7 each have a two-step structure in thepresent invention, they may have a step structure of three or moresteps. In this case, a surface contacting the buffer layer 4 is thefirst lower surface, and surfaces that do not contact the buffer layer 4are all the second lower surfaces. Further, the lower part 7 b of thesignal electrode 7 and the lower part 8 b of the first ground electrode8 may have a tapered shape in which the widths thereof are graduallyreduced toward the first and second optical waveguides 10 a and 10 b,respectively.

Further, although the second ground electrode 9 does not have the stepstructure in the above embodiment, it may have the step structure, or apart of the second ground electrode 9 may be embedded in the openingformed in the insulating layer 5.

Examples

Simulation was performed to calculate the wavelength chirp α of themodulated light of the optical modulator when the thickness T of thelower part 8 b of the first ground electrode 8 (i.e., thickness of theinsulating layer 5) was set as a variable parameter. The thickness ofthe waveguide layer 2 made of the lithium niobate film including theridge 2 r (i.e., total thickness of the waveguide layer 2 and theprotective layer 3) was 1.5 μm, the ridge width (W₀) was 1 μm, thethickness of the buffer layer 4 was 0.9 μm, and the dielectric constantof the buffer layer 4 was 13. The electrode layer 6 including the signalelectrode 7 and first and second ground electrodes 8 and 9 was made ofAu, and the maximum thickness thereof was 11 μm. The width W₁₀ of theupper part 7 a of the signal electrode 7 and the width W₁₁ of the lowerpart 7 b were both 3 μm.

The thickness T of the lower part 8 b of the first ground electrode 8(i.e., thickness of the insulating layer 5) as the variable parameterwas set to eight values: 0 μm (no step), 0.5 μm, 1 μm, 2 μm, 3 μm, 4 μm,5 μm, and 6 μm. The width W₂₁ of the lower part 8 b of the first groundelectrode 8 was 3 μm (step height T #0). The gap G₂ between the signalelectrode 7 and the first ground electrode 8 was 7 μm, and gap G₃between the signal electrode 7 and the second ground electrode 9 was12.5 μm.

FIGS. 6A and 6B each illustrate an equipotential surface which is anexample of a result obtained by the simulations. FIG. 6A illustrates aresult when T is set to 0 μm, and FIG. 6B illustrates a result when T isset to 6 μm. The interval between the equipotential lines around thesecond optical waveguide 10 b is smaller when T=6 μm, revealing that anelectric field is stronger there.

FIG. 7 is a graph illustrating a calculation result of the wavelengthchirp α. As illustrated in FIG. 7, in the case of a conventionalstructure (see FIG. 9C) where no step is formed (T=0 μm), the absolutevalue of the wavelength chirp α is as large as 0.36. When T is largerthan 0 μm, that is, when the first ground electrode 8 has two lowersurfaces having different heights, and the lowest surface is in contactwith the upper surface of the buffer layer 4, the absolute value of thewavelength chirp α can be reduced. This is mainly because an electricfield to be applied to the right-side second optical waveguide 10 bbecomes large by increasing the step height T.

Then, simulation was performed to calculate the wavelength chirp α ofthe modulated light of the optical modulator when the width W₁₁ of thelower part 7 b of the signal electrode 7 (i.e., width of the first lowersurface S₁₁) was changed. The thickness T of the insulating layer 5 was2 μm, and the thickness of the electrode layer 6 was 4 μm. The width W₂₁of the lower part 8 b of the first ground electrode 8 was 3 μm. Thewidth W₁₁ of the lower part 7 b of the signal electrode 7 as thevariable parameter was set to four values: 3 μm, 4 μm, 5 μm, and 6 μm.The width W₁₀ of the upper part 7 a of the signal electrode 7 was 15 μm.

FIG. 8 is a graph illustrating a calculation result of the wavelengthchirp α. As illustrated in FIG. 8, when the width W₁₁ of the lower part7 b of the signal electrode 7 is changed, the wavelength chirp α islinearly changed and becomes 0 when the width W₁₁ is about 6 μm. Sincethe width W₂₁ of the lower part 8 b of the first ground electrode 8 is 3μm, it can be seen that a condition for achieving chirp-free is that thewidth W₁₁ of the lower part 7 b of the signal electrode 7 is larger thanthe width W₂₁ of the lower part 8 b of the first ground electrode 8. Asdescribed above, the first and second lower surfaces S₁₁ and S₁₂ havingdifferent heights are formed in the signal electrode 7, and the widthW₁₁ of the first lower surface S₁₁ of the signal electrode 7 in contactwith the upper surface of the buffer layer 4 is controlled to finelyadjust the magnitude of an electric field to be applied to the firstoptical waveguide 10 a, whereby the wavelength chirp α can be reduced tosubstantially 0.

Then, simulation was performed to calculate the wavelength chirp α ofthe modulated light of the optical modulator shown in FIG. 4A in which apart of the insulating layer 5 existing below the electrode isolationregion 6 i between the signal electrode 7 and the first ground electrode8 had been removed. The thickness of the waveguide layer 2 made of thelithium niobate film including the ridge 2 r (i.e., total thickness ofthe waveguide layer 2 and protective layer 3) was 1.5 μm, the ridgewidth (W₀) was 1.2 μm, the thickness of the buffer layer 4 was 0.9 μm,and the dielectric constant of the buffer layer 4 was 13. The electrodelayer 6 including the signal electrode 7 and first and second groundelectrodes 8 and 9 was made of Au. The thickness of each of the upperpart 7 a of the signal electrode 7 and the upper part 8 a of the firstground electrode 8 (i.e., thickness of the electrode layer 6) was 4 μm.The thickness T of each of the lower part 7 b of the signal electrode 7and the lower part 8 b of the first ground electrode 8 (i.e., thicknessof the insulating layer 5) was 3 μm.

The width W₁₀ of the upper part 7 a of the signal electrode 7 was 34 mm,and the width W₁₁ of the lower part 7 b was 4 μm. The width W₂₀ of theupper part 8 a of the first ground electrode 8 was 203 μm, and the widthW₂₁ of the lower part 8 b was 3 μm. The width W₃₀ of the second groundelectrode was 200 μm. The gap G₂ between the signal electrode 7 and thefirst ground electrode 8 was 8.5 μm, and gap G₃ between the signalelectrode 7 and the second ground electrode 9 was 60 μm.

As a result of the simulations under the above conditions, thehalf-wavelength voltage of 2.5 V at 32 GHz, a bandwidth of 45 GHz, and awavelength chirp α of 0.02 were obtained in an interaction length of 25mm. Thus, a reduced wavelength chirp, a low drive voltage, and goodfrequency characteristics were obtained.

REFERENCE SIGNS LIST

-   1 substrate-   2 waveguide layer-   3 protective layer-   4 buffer layer-   5 insulating layer-   6 electrode layer-   7 signal electrode-   7 a upper part of the signal electrode-   7 b lower part of the signal electrode-   7 e one end of the signal electrode-   7 g other end of the signal electrode-   8 first ground electrode-   8 a upper part of the first ground electrode-   8 b lower part of the first ground electrode-   9 second ground electrode-   10 Mach-Zehnder optical waveguide-   10 a first optical waveguide-   10 b second optical waveguide-   10 c branch section-   10 d multiplexing section-   10 e ₁ first linear section of the Mach-Zehnder optical waveguide-   10 e ₂ second linear section of the Mach-Zehnder optical waveguide-   10 e ₃ third linear section of the Mach-Zehnder optical waveguide-   10 f ₁ first curved section of the Mach-Zehnder optical waveguide-   10 f ₂ second curved section of the Mach-Zehnder optical waveguide-   12 terminal resistors-   21 sapphire substrate-   22 a first optical waveguide-   22 b second optical waveguide-   23 buffer layer-   24 a, 24 a ₁, 24 a ₂ signal electrode-   24 b, 24 c 24 d ground electrode-   100, 200, 300, 400, 500, 600, 700, 800 optical modulator-   G₂ gap between the signal electrode and the first ground electrode-   G₃ gap between the signal electrode and the second ground electrode-   S₁₁ first lower surface of the signal electrode (lower surface of    the lower part 7 b)-   S₁₂ second lower surface of the signal electrode (upper surface of    the lower part 7 a)-   S₂₁ lower surface of the first ground electrode (lower surface of    the lower part 8 b)-   S₂₂ lower surface of the second ground electrode (lower surface of    the upper part 8 a)-   Si input light-   So modulated light (output light)-   W₀ width of each of the first and second optical waveguides (ridge    width)-   W₁₀ entire width of the signal electrode-   W₁₁ width of the first lower surface of the signal electrode-   W₁₂ width of the second lower surface of the signal electrode-   W₂₀ entire width of the first ground electrode-   W₂₁ width of the first lower surface of the first ground electrode-   W₂₂ width of the second lower surface of the first ground electrode-   W₃₀ entire width of the second ground electrode

What is claimed is:
 1. An optical modulator comprising: a Mach-Zehnderoptical waveguide including first and second optical waveguides; abuffer layer covering the first and second optical waveguides; and anelectrode layer including first and second ground electrodes and asignal electrode positioned between the first and second groundelectrodes in a plan view, wherein an insulating layer provided betweenthe buffer layer and the electrode layer, the insulating layer havingfirst and second openings positioned above the first and second opticalwaveguides, respectively, the signal electrode has a first lower surfacecovering the first optical wave guide through the buffer layer, thesignal electrode including an upper part formed in the electrode layerand a lower part embedded in the first opening, and the first groundelectrode has a first lower surface covering the second opticalwaveguide through the buffer layer and a second lower surface positionedabove the first lower surface thereof, the first ground electrodeincluding an upper part formed in the electrode layer and a lower partembedded in the second opening, wherein a gap between the signalelectrode and the second ground electrode is larger than a gap betweenthe signal electrode and the first ground electrode, and wherein a widthof the upper part of the first ground electrode is larger than a widthof the lower part of the first ground electrode.
 2. The opticalmodulator as claimed in claim 1, wherein a width of the first lowersurface of the signal electrode is larger than a width of the firstlower surface of the first ground electrode.
 3. The optical modulator asclaimed in claim 1, wherein the signal electrode further has a secondlower surface positioned above the first lower surface thereof.
 4. Theoptical modulator as claimed in claim 1, wherein the width of the firstlower surface of the signal electrode and the width of the first lowersurface of the first ground electrode are larger than the widths of thefirst and second optical waveguides.
 5. The optical modulator as claimedin claim 1, wherein at least a part of the insulating layer existing atthe lower portion of an electrode isolation region between the lowerpart of the signal electrode and the lower part of the first groundelectrode is removed.
 6. The optical modulator as claimed in claim 1,wherein the Mach-Zehnder optical waveguide has at least one linearsection and at least one curved section, the first lower surface of thesignal electrode covers the first optical waveguide at the linearsection through the buffer layer, and the first lower surface of thefirst ground electrode covers the second optical waveguide at the linearsection through the buffer layer.
 7. The optical modulator as claimed inclaim 1, wherein the Mach-Zehnder optical waveguide is formed of alithium niobate film formed on a substrate, and the c-axis of thelithium niobate film is oriented in a direction perpendicular to a mainsurface of the substrate.